Question

If a^2-5a+1 =0 Then find a^2+(1/a)^2​
Answer fast.

Answer 1

Answer:

23

Step-by-step explanation:

a² - 5a + 1 = 0

Transposing 5a to RHS

⇒ a² + 1 = 5a

Transposing a to LHS

⇒ ( a² + 1 ) / a = 5

⇒ a²/a + 1/a = 5

⇒ a + 1/a = 5

Squaring on both sides

⇒ ( a + 1/a )² = 5²

Since ( x + y )² = x² + y² + 2xy

⇒ a² + 1/a² +2( a )( 1/a ) = 25

⇒ a² + 1/a² + 2 = 25

Transposing 2 to RHS

⇒ a² + 1/a² = 25 - 2

⇒ a² + 1/a² = 23

Hence the value of a² +1/a² is 23.